The present invention relates to a three-dimensional image constructing method in which a plurality of tomographic images, for example, obtained by an X-ray computerized tomography (CT) apparatus or obtained by decomposing a volume image measured three-dimensionally by an MRI apparatus are stacked up to thereby obtain a stacked three-dimensional image (three-dimensional original image) and then two-dimensional images obtained by observing the stacked three-dimensional image from arbitrary directions are shaded to construct a three-dimensional image (which means an image constituted by two-dimensionally arranged pixels but made to look like a three-dimensional image by shading).
The three-dimensional image constructing method of this type is known heretofore. As a conventional method, a parallel projection method is used for transformation of coordinates of pixels into a coordinate system of a projection plane equivalent to a display screen.
The parallel projection method used conventionally for transformation of coordinates of pixels is effective for constructing a three-dimensional image obtained by observing a subject such as for example an internal organ, or the like, from the outside of the subject. The method is however unsuitable for constructing a three-dimensional image obtained by observing the subject from the inside (that is, by placing a view point in the inside of the subject). Accordingly, the conventional parallel projection method cannot satisfy the demand that three-dimensional images should be obtained as if the inside of the subject was observed through an endoscope.
Therefore, a three-dimensional image constructing method disclosed in Japanese application No. 6-3492, which is one of the Japanese priority applications of U.S. application Ser. No. 08/374,088 which has been incorporated herein by reference, has been developed. This is a method in which transformation of coordinates of pixels on each tomographic image into coordinates on a projection plane is performed by using a central projection method to thereby project each tomographic image onto the projection plane; and pixel values are given to the coordinates of pixels on the projection plane in accordance with a shading algorithm to perform shading to thereby construct a three-dimensional image. Referring to FIG. 1, this three-dimensional image constructing method will be described below.
FIG. 1 is a view for explaining the coordinate transformation based on central projection method and shows that projection of a point S(x0, z0, y0) on a tomographic image 30 onto a projection plane 20 results in a point P(x, y, z) on the projection plane 20. Assume now that a plurality of tomographic images 30 (#1, #2, . . . , #n) exist in practice.
In FIG. 1, at the time of projection of a tomographic image 30 onto the projection plane 20 according to the central projection method, the coordinates of pixels of the tomographic image 30 are transformed into coordinates on the projection plane 20 as follows.
Here, a represents a point of intersection of the x axis and the projection plane 20, b represents a point of intersection of the y axis and the projection plane 20, and c represents a point of intersection of the z axis and the projection plane 20.
Further, a represents an angle between the x axis and a line obtained through projection, onto the z-x plane, of a perpendicular from the origin to the projection plane 20; xcex2 represents an angle between the above-mentioned perpendicular and the x-z plane; a point e(x1, y1, z1) represents the position of a view point e: a point P(x, y, z) represents a point on the projection plane (equivalent to the display screen) 20; and a point S(x0, z0, y0) represents a point of intersection of the tomographic image 30 and a line 22 passing through the point e(x1, y1, z1) and the point P(x, y, z).
Under the aforementioned definition, the following equations hold.
First, the projection plane 20 is given by the equation:
(x/a)+(y/b)+(z/c)=1xe2x80x83xe2x80x83(1)
Further, the line 22 passing through the point e(x1, y1, z1) and the point P(x, y, z) is given by the equation:                                                                                           (                                      x0                    -                    x                                    )                                /                                  (                                      x1                    -                    x                                    )                                            =                                                (                                      y0                    -                    y                                    )                                /                                  (                                      y1                    -                    y                                    )                                                                                                        =                                                (                                      z0                    -                    z                                    )                                /                                  (                                      z1                    -                    z                                    )                                                                                        (        2        )            
When the projection plane 20 is drawn through a point C1(xc1, yc1, zc1), the values z, x and y are given by the following equations:
z=[Xxc2x7k1xe2x88x92Yxc2x7k2xe2x88x92yc1xc2x7k3xe2x88x92{(cixc2x7k3xc2x7zc1)/bi}+{(aixc2x7k3xc2x7X)/(bixc2x7cos xcex1)}xe2x88x92{(aixc2x7k3xc2x7xc1)/bi}]/[1xe2x88x92{(cixc2x7k3)/bi}+{(aixc2x7k3xc2x7sin xcex1)/(bixc2x7cos xcex1)}]xe2x80x83xe2x80x83(3)
x=(Xxe2x88x92zxc2x7sin xcex1)/cos xcex1xe2x80x83xe2x80x83(4)
y=[yc1+{xe2x88x92cixc2x7(zxe2x88x92zc1)xe2x88x92aixc2x7(xxe2x88x92xc1)}]/bixe2x80x83xe2x80x83(5)
in which k1=sin xcex1, k2=cos xcex1/sin xcex2, k3=cos xcex1xc2x7cos xcex2/sin xcex2, ai=1/a, bi=1/b, and ci=1/c.
Here, as the aforementioned point C1(xc1, yc1, zc1), for example, a point of intersection of a perpendicular drawn from the view point e(x1, y1, z1) to the projection plate 20 and the projection plane 20 may be used under the conditions as follows:
zc1=z1xc2x1[h/sqrt{1+(c2/a2)+(c2/b2)}](xe2x80x9cxe2x88x92xe2x80x9d in xe2x80x9cz1xc2x1xe2x80x9d is valid in the case of z0 less than zc1)xe2x80x83xe2x80x83(6)
xc1=x1+{cxc2x7(z1xe2x88x92zc1)/a}xe2x80x83xe2x80x83(7)
xe2x80x83yc1=y1+{cxc2x7(z1xe2x88x92zc1)/b}xe2x80x83xe2x80x83(8)
in which h represents the length of the perpendicular from the view point e(x1, y1, z1) to the projection plane 20.
When the projected image is expressed with 512 pixels by 512 pixels on the display screen (not shown) equivalent to the projection plane 20, each of X and Y takes values of xe2x88x92256 to +256. Values of x and y are determined correspondingly to the respective values of X and Y in accordance with the aforementioned equations (3), (4) and (5). Because x1, y1 and z1 of the point e are given freely, coordinates x0 and z0 of the pixel point S on the tomographic image y0=d0 are determined in accordance with the following equations (9) and (10).
x0={(d0xe2x88x92y)/(y1xe2x88x92y)}xc3x97(x1xe2x88x92x)+xxe2x80x83xe2x80x83(9)
z0={(d0xe2x88x92y)/(y1xe2x88x92y)}xc3x97(z1xe2x88x92z)+zxe2x80x83xe2x80x83(10)
Because d0 takes a plurality of values correspondingly to the plurality of tomographic images, a plurality of points (x0, z0) to be projected are determined correspondingly to one combination of X and Y on the projection plane.
In FIG. 1, L represents the distance from the view point e to the point S, and L is a parameter for obtaining the pixel value (luminance) of the point P. The pixel value of the point P is proportional to a value obtained by subtracting the above L from the maximum pixel value L max which is set in advance. As the value of L maxxe2x88x92L increases, the density on the screen is made bright.
The aforementioned coordinate transformation is performed with respect to all the points on the projection plane 20 equivalent to the display screen. Further, the aforementioned coordinate transformation is performed with respect to all the tomographic images 30.
Further, shading is performed so that a scenographic feeling is given to construct a three-dimensional image when the tomographic images are displayed on a two-dimensional display screen. A predetermined shading algorithm, for example, a depth method, is used for shading, so that pixel values are given to coordinates of respective pixels on the projection plane 20 in accordance with the shading algorithm.
According to the method of FIG. 1, a three-dimensional image can be obtained as if the inside of a subject is observed through an endoscope, because projection lines spread out radially from the view point.
The aforementioned method is however premised on the assumption that the view point e is placed in a space originally open in the inside of a subject such as an esophagus, a trachea, an intestine, or the like. Accordingly, it is impossible to construct such a three-dimensional image as seen when the inside (having an area) of a subject is peeped into through a small hole. Particularly, as shown in FIG. 2, it is impossible to construct a three-dimensional image as seen when a subject 26 is observed through a peritoneoscope 25 inserted into the subject 26. The method cannot meet the demand to obtain such images.
An object of the present invention is to provide a three-dimensional image constructing method which makes it possible to obtain a three-dimensional image as if the inside (having an area) of a subject was peeped into through a small hole, particularly, a the three-dimensional image as if the inside of a subject was observed through a peritoneoscope inserted into the subject.
The foregoing object of the present invention is achieved by a three-dimensional image constructing method in which a plurality of tomographic images including volume images are stacked to thereby obtain a stacked three-dimensional image, and a two-dimensional image obtained by observing the stacked three-dimensional image from an arbitrary direction is shaded to thereby construct a three-dimensional image, in which at the time of projection of each of the tomographic images onto a projection plane, coordinates of pixels in the tomographic image are transformed into coordinates on the projection plane by using central projection method and then shading is performed by giving pixel values to the coordinates of pixels on the projection plane in accordance with a shading algorithm to thereby construct a three-dimensional image, and in which a predetermined region containing a point of view is set in advance so that coordinate transformation according to the central projection method and shading are applied not to coordinates of pixels within the region but only to coordinates of pixels out of the region.
That is, the present invention can be expressed as follows.
A method of constructing a three-dimensional image by using a central projection method, including the steps of:
(a) setting coordinates of a point of view on a memory space so that a projection subject image is located between the view point and a plane of projection;
(b) setting a predetermined region containing said view point;
(c) judging whether coordinates of a pixel to be projected are in said predetermined region or not; and
(d) applying coordinate transformation according to the central projection method and shading to the coordinates of the pixel to be projected only when the coordinates of the pixel are out of said predetermined region, while the coordinate transformation according to the central projection method and shading are not applied to the coordinates of the pixel to be projected when the coordinates of the pixel are in said predetermined region.
Because the set region containing the view point serves as a small hole and because a central projection method is used for transformation of coordinates of pixels in the tomographic image, a larger image than the size of the hole can be seen.
Accordingly, it is made possible to obtain a three-dimensional image as if the inside (having an area) of a subject was peeped into through a small hole and, particularly, a three-dimensional image as if the inside of a subject 26 was observed through a peritoneoscope 25 inserted into the subject 26 as shown in FIG. 2.